Britain's Prime Minister Theresa May, Yemeni President Abd Rabu Mansour Hadi, Cuban President Miguel Diaz-Canel and Zimbabwean President Emmerson Dambudzo Mnangagwa are among those expected to take to the podium.
Trump will meet with one of his strongest allies, Israeli Prime Minister Benjamin Netanyahu, at 1300 GMT, according to a Netanyahu spokesman. The two leaders are among the fiercest critics of Iran's nuclear program, and Netanyahu has applauded Trump's decision to move the US embassy to Jerusalem.
Trump will chair a UN Security Council meeting for the first time, with US Ambassador to the UN Nikki Haley saying it could be the "most-watched Security Council meeting ever," in comments ahead of Trump's UN visit.
The meeting, scheduled for 1400 GMT, is expected to focus on Iran but was officially scheduled under the title of "non-proliferation of weapons of mass destruction."
Other world leaders from the countries of the 15-member council expected to speak include Britain's May, France's Emmanuel Macron, Polish President Andrzej Dude, Bolivia's Evo Morales and Mark Rutte from the Netherlands.
Meetings on several major UN issues are scheduled. The level of US involvement in these events is unclear, and some of them relate to agreements or UN agencies out of which the Trump administration has withdrawn the country.
UN Secretary General Antonio Guterres is hosting a closed-door meeting on climate change at 1500 GMT, with Britain’s Theresa May and France’s Emmanuel Macron expected to attend.
France, Germany and the Office of the United Nations High Commissioner for Human Rights (OHCHR) are hosting a meeting at 1530 GMT to mark the 70th anniversary of the universal declaration of human rights. The US has announced plans to withdraw from the UN's Human Rights Council, which is part of OHCHR.
And at 1800 GMT, there will be a meeting on the UN’s global compact on migration, which is due to be adopted in Marrakech in December. Every UN member state has agreed to it apart from the US and Hungary.
The UN is also holding its first high-level meeting on tuberculosis (TB) throughout the day, and hopes to agree on a political declaration to step up progress in eliminating the global TB epidemic.